Uncooled, perforated sheet metal flameholders have various hole patterns to control the flow of fuel-air mixture therethrough but as such frequently over heat at high engine pressures and temperatures with resulting failure. Replacement with a double walled cooled structure the walls of which are secured together as a unit requires that the flameholder operate at a low temperature to avoid thermal fatigue, local unbonding and joint cracking because of the high thermal difference between inner and outer walls. The present invention provides the double wall, cooled construction but permits high temperature operation by supporting the inner wall within the outer wall without constraining relative thermal expansion between the walls. This invention permits a cooled flameholder without the thermal loading problems.